# From Circuit Evidence to Mechanistic Theory: An Inductive Logic Approach

arXiv: https://arxiv.org/abs/2605.21303 · HTML: https://mlsanity.com/paper/2605.21303/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 20 May 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Reasoning Circuits in Language Models: A Mechanistic Interpretation of Syllogistic Inference](https://mlsanity.com/paper/2408.08590/) (2024)
- [The Emergence of Abstract Thought in Large Language Models Beyond Any Language](https://mlsanity.com/paper/2506.09890/) (2025)
- [A Implies B: Circuit Analysis in LLMs for Propositional Logical Reasoning](https://mlsanity.com/paper/2411.04105/) (2024)
- [Beyond Code Generation: LLM-supported Exploration of the Program Design Space](https://mlsanity.com/paper/2503.06911/) (2025)
- [Are formal and functional linguistic mechanisms dissociated in language models?](https://mlsanity.com/paper/2503.11302/) (2025)
- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [Validating Mechanistic Interpretations: An Axiomatic Approach](https://mlsanity.com/paper/2407.13594/) (2024)
- [TRACE: Training and Inference-Time Interpretability Analysis for Language Models](https://mlsanity.com/paper/2507.03668/) (2025)
- [Emergence and Localisation of Semantic Role Circuits in LLMs](https://mlsanity.com/paper/2511.20910/) (2025)

## Built on by (most cited first, 1 of 1)

- [Align, Unify, Suppress, Route: A Coherentist View of Transformer Computation](https://mlsanity.com/paper/2608.22034/) (2026)

## Abstract (arXiv)

Mechanistic interpretability produces circuit-level causal analyses of neural network behaviour, but discovered circuits often remain isolated experimental artefacts: there is no shared formal representation for what circuits compute, how they relate, or when two findings provide evidence for the same mechanism. This work provides a formal infrastructure for cumulative mechanistic science by treating circuit interpretation as inductive theory construction. Each circuit is characterised at two levels: a Causal Functional Signature (CFS), which grounds component behaviour in causal attribution evidence and token role profiles, and an architectural signature τarch, learned by inductive logic programming (ILP) from scale-invariant structural predicates. Together, these constitute a formal coherence layer that makes mechanistic claims explicit, comparable via θ-subsumption, and portable across model scales. CFS reveals qualitatively distinct computational strategies across task types, including attention-mediated copying versus MLP-mediated binding. ILP signatures achieve substantially better structural separation than graph kernel and feature-vector baselines, and support principled transfer across model scales and architecture families.